Physics Letters B 774 (2017) 575–581
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Loop induced type-II seesaw model and GeV dark matter with
U (1)
B−L
gauge symmetry
Takaaki Nomura
a,∗
, Hiroshi Okada
b
a
School of Physics, KIAS, Seoul 02455, Republic of Korea
b
Physics Division, National Center for Theoretical Sciences, Hsinchu, 300, Taiwan
a r t i c l e i n f o a b s t r a c t
Article history:
Received
1 August 2017
Received
in revised form 15 October 2017
Accepted
15 October 2017
Available
online xxxx
Editor:
J. Hisano
We propose a model with U (1)
B−L
gauge symmetry and several new fermions in no conflict with
anomaly cancellation where the neutrino masses are given by the vacuum expectation value of Higgs
triplet induced at the one-loop level. The new fermions are odd under discrete Z
2
symmetry and
the lightest one becomes dark matter candidate. We find that the mass of dark matter is typically
O(1)-O(10) GeV. Then relic density of the dark matter is discussed.
© 2017 Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Radiative neutrino mass models are widely renown in con-
necting
the neutrino masses and a dark matter (DM) candidate
at low energy theory, which are also applied to accommodate
some experimental anomalies that cannot be explained by the
standard model (SM). Thus many authors have historically been
working along these ideas; for example, refs. [1–91] mainly focuses
on
the neutrino mass scenarios realized at one-loop level, and
refs. [92–94] discuss the systematic analysis of (Dirac) neutrino os-
cillation,
charged lepton flavor violation, and collider physics in the
framework of neutrinophilic and inert two Higgs doublet model
(THDM), respectively.
A
Higgs triplet model (HTM) is also an interesting scenario
to get non-zero neutrino masses where these masses are in-
duced
by the vacuum expectation value (VEV) of an SU(2)
L
triplet
Higgs field, , and this scenario is also called as type-II seesaw
model [95,96]. The VEV of the Higgs triplet, v
, is required to be as
small as v
3GeV from the electroweak precision measurement;
especially that of ρ-parameter. In the Higgs triplet model, we con-
sider
the triplet has electroweak scale mass term μ
2
Tr[
†
]
which does not induce VEV of the triplet due to positive μ
2
in
contrast to the case of SM Higgs. The VEV of Higgs triplet is in-
duced
via H
T
H interaction with coupling μ as v
∝ μv
2
/m
2
where v is the VEV of the SM Higgs field and μ is assumed to be
smaller than electroweak scale to get a small value of v
. How-
*
Corresponding author.
E-mail
addresses: nomura@kias.re.kr (T. Nomura),
macokada3hiroshi@cts.nthu.edu.tw (H. Okada).
ever the value of parameter μ is not theoretically restricted and
can be large.
In
ref. [17], the authors have introduced a model that theo-
retically
realizes a small value of v
. In this scenario, the H
T
H
interaction
is forbidden at tree level by global B −L symmetry but
it is allowed by an one-loop effect where lepton number violation
is included and scalar bosons with Z
2
odd parity propagate inside
the loop.
It
is also interesting to construct such a model with U(1)
B−L
gauge symmetry since it leads rich phenomenology. In this case,
we need to add several SM singlet fermions with B − L charge to
cancel gauge anomalies, and it would be motivated to generate the
tiny v
by a loop diagram containing propagators of fermions with
Z
2
odd parity which can be a DM candidate. In addition, we would
have some predictions for DM mass when Z
2
odd neutral fermion
masses are related to v and v
.
In
this paper, we propose a neutrino model with Higgs triplet
field where v
is arisen at the one-loop level and we interpret this
mechanism as a theoretical reason why v
is so small. To achieve
the mechanism, we impose U (1)
B−L
gauge symmetry to forbid
H
T
H interaction at tree level and introduce several new fermions
instead of scalar fields in no conflict with anomaly cancellation.
Then v
is induced via one-loop diagram with new fermion prop-
agators
after spontaneous breaking of gauge symmetries. Moreover,
we find the typical mass scale of DM is around 1 − 10 GeV, since
it is proportional to v
due to a specific structure of the neutral
fermion mass matrix. Then we show the mechanism to generate
the neutrino masses and analyze such a tiny mass of the fermionic
DM candidate.
This
paper is organized as follows. In Sec. 2, we show our
model, and formulated the neutral fermion sector, boson sector,
https://doi.org/10.1016/j.physletb.2017.10.033
0370-2693/
© 2017 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
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